GPT-5.6 is a rewrite of mathematical history in a single day, breaking the eight-year record set by

  It's the first time in the history of the world.

Just recently, AI has solved a mathematical problem.

Jared Duker Lichtman, assistant professor of mathematics at Stanford University, confirmed that:In just one day, the GPT-5.6 broke the record set by the Taoiseach's five-man team of Large Prime Gaps for eight years!

Not only that, it proposes an unprecedented new constructed flag."Skewed Residue Classes" and "Skewed Residue Classes"And in giving proof,That day.It has been formally validated by machines in the Lean language.

This means that when human mathematicians are still trying to understand the complex logic of "digesting", the machines have been sealed to confirm:The theory has been proven to be correct, man, and you are still behind.

To understand how great this breakthrough of GPT-5.6 is, we must first explore a mathematical phantom that has plagued humanity for thousands of years.Question of the distribution of prime numbers。

The prime numbers ((2, 3, 5, 7, 11...) are like solitary planets scattered throughout the whole universe.

They can only be solved by 1 and themselves, the "atoms" that make up all the numbers.

However, the distribution of these "atoms" is not regulated.

As the numbers get bigger, the prime numbers become increasingly rare.

In other words, the distance between two adjacent prime numbers increases.

Here, mathematicians divide the two main classes, exploring the two extremes of prime distribution:

Part One: Find the smallest distance (minimal number of gaps)。

They tried to prove that even in the infinite depths of the universe, there is still a "number of microbes" that are very close.

In 2013, an anonymous Chinese mathematicianZhang Yi-dongThe birth of space proves that there are infinitely many primes less than 70 million at a distance and shocks the world.

This is the famous problem of the "parametric number gap".

Afterwards, mathematicians worked together to continuously optimize the result, eventually advancing it to 246.

Recently, AI mathematician AxiomProver has given a formalized verification.

Part Two: Searching for the Largest Desert。

Their problem is quite the opposite: since prime numbers are becoming increasingly rare, between two prime numbers, there are two prime numbers.How big can this "digital desert without prime numbers" be?

This is the famous "Fourth Problem of Paul Erdős".

If Zhang Yi-dong is looking for two adjacent oases in the Yangtze Desert, then those who explore the prime gap are looking for the longest, driest, most desperate area without oases in the desert.

Over the years, humans have struggled to measure the length of this "largest desert".

In 2014, humanity sent an unprecedentedIt's called the League of Mathematical Avengers.(Polymath Project) This five-person group includes:

The winner of the Fields Prize, one of the world's greatest mathematical geniuses, Terence Tao, another Fields Prize winner, analytic mathematician James Maynard, and three mathematicians: Kevin Ford, Ben Green, and Sergei Konyagin.

The five mathematicians worked together, for about five years, to push the lower bound of the prime number gap to a new limit, giving a complex formula.

This result is considered to be the pinnacle of recent decades, and it is widely believed that the record will not be shaken for decades to come.

Until the GPT-5.6 presses the "return" button.

The mathematics research team at Stanford University was stunned by the verification process.

GPT-5.6 doesn't rely on brute force computation like traditional leverage programs, but it exhibits an awkward "mathematical intuition".

According to the published paper,The new boundary of GPT-5.6 was lower than the results of a group of five people, including Tao Te Ching, in 2018, with hardcore students saving one.\log_3(n)The cause!

For non-mathematical readers, all you need to know is that in particle number theory, improving a pair of logs is no less difficult than finding a new fundamental particle in physics.

In order to optimize for these subtle factors, the Tao Te Ching team ran out of human mathematical toolkits that year. And \log\log\log\log\n) The triple pairs are extremely stubborn, like a lock embedded in a gene that human mathematicians have tried for eight years to build without a tree.

But GPT-5.6 not only optimizes it, but it's also recognized as one of the best in the world.The largest quantitative advance in the field of prime numbers gaps in recent years!

How is it done?

In the process of proofing, GPT-5.6 created a trick that has never appeared in human mathematical literature."Skewed Residue Classes" and "Skewed Residue Classes"。

In past proofs, human mathematicians have often used the traditional "Sieve Theory", combined with Maynard's Weights weighting system, to filter out non-prime numbers and thus construct long "compound intervals".

It's like fishing a net with a net-eye rule.

GPT-5.6's "trending residual class" is just like this fishing net.Gavi's field of torsion。

It cleverly avoids certain symmetrical disorders that lead to inefficiency by applying "biasing" at a microscopic level to the traditional method of inference.

Then, like a commander of a thousand horsemen, it constructed this whole new slope, with the improved weight of Maynard, and the incredibly sophisticated.The theory of supergraph coverage (hypergraph covers)It's a perfect match.

Eventually, the miracle was born: on the same scale, GPT-5.6 successfully built more than humans could at the time.The prime-free gap is also much longer than the prime-free gap.！

In the traditional mathematical world, if a mathematician claims to have solved a world-class problem, such as the previous telescope to prove ABC's conjecture, it would be costly for peers to review and understand his proof thinking.A few yearsMathematicians need to hold workshops to check the formula step by step.

But GPT-5.6 didn't give humans the chance to breathe.It's easy to translate the entire proof into the Lean 4 language, while giving proof of human reading!

What is Lean?

It is currently the most authoritative proof of the interactive theorem in mathematics.

As long as a proof of code can run through Lean's compiler without a red flag error, the theorem is 100% logically valid.

Ben Green, a professor of mathematics at the University of Oxford who was working with Taotzeev at the time, spent several hours thinking and talking to two collaborators, Felts owner Taotzeev and James Maynard, to basically determine that the proof was correct.

But he was surprised by the speed with which it was formalised.

A funny thing happened on the way:

On the one hand, there is a complete but almost unreadable proof that its authors are still anonymous (the paper's authorship is ChatGPT); on the other hand, there is formal verification by Lean, so we know that it is logically stable; and experts in this field are also basically able to understand the key ideas and proof logic on an informal level.

This is an increasingly common situation.

However, he also acknowledged that it would take at least a few weeks of effort to move from this state to a complete, human-readable and human-written paper in the traditional sense.

It's like this.Machine proof of the enormous contrast between human digestionMathematical research officially entered a new era.

Many people shouted that the game was dead when AlphaGo defeated Lee Seung-soo with the "One Hand of God" (Hand 37), but it turned out that the game was not dead, and today's top players are learning the game of AI to reach an unprecedented level of tactics.

Today, the storm has finally reached the area of pure mathematics known as the "Pearl in the Crown of Science".

GPT-5.6 rewrite Zhang Yi-dong's reputation as a record in the relevant field, breaking the rule of the Tao Te Ching team, which is not human grief but human honour.

It is part of the "New Age of Sailing", a new era in which carbon-based life and hydrogen-based life are at war with each other.The curtain has been officially opened.